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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 11 Dec 2009 01:44:57 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/11/t126052113293c75pi4df2mdg8.htm/, Retrieved Mon, 29 Apr 2024 03:00:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65886, Retrieved Mon, 29 Apr 2024 03:00:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact154
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency ...] [2009-12-11 08:44:57] [5d37783481a916b2505b66314b556267] [Current]
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Dataseries X:
17903.9
16379.4
15420.3
17870.5
15912.8
13866.5
17823.2
17872
17422
16704.5
15991.2
16583.6
19123.5
17838.7
17209.4
18586.5
16258.1
15141.6
19202.1
17746.5
19090.1
18040.3
17515.5
17751.8
21072.4
17170
19439.5
19795.4
17574.9
16165.4
19464.6
19932.1
19961.2
17343.4
18924.2
18574.1
21350.6
18594.6
19823.1
20844.4
19640.2
17735.4
19813.6
22160
20664.3
17877.4
20906.5
21164.1
21374.4
22952.3
21343.5
23899.3
22392.9
18274.1
22786.7
22321.5
17842.2
16373.5
15993.8
16446.1
17729




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65886&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65886&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65886&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18671.7163934426277.6037185994167.2603252133897
Geometric Mean18549.5284860081
Harmonic Mean18428.9071039383
Quadratic Mean18795.1276279776
Winsorized Mean ( 1 / 20 )18677.0950819672267.76713643025069.7512597362089
Winsorized Mean ( 2 / 20 )18680.8032786885264.39709004424570.6543452333852
Winsorized Mean ( 3 / 20 )18685.6573770492254.84945330430473.320374577133
Winsorized Mean ( 4 / 20 )18686.1163934426252.79790875938173.9172111238803
Winsorized Mean ( 5 / 20 )18673.0918032787249.63235768147674.802369279006
Winsorized Mean ( 6 / 20 )18612.6983606557229.84071741042080.9808573970797
Winsorized Mean ( 7 / 20 )18620.6049180328227.42916189425881.8743065442519
Winsorized Mean ( 8 / 20 )18634.8081967213224.66265237728682.945732187952
Winsorized Mean ( 9 / 20 )18609.2098360656219.28550592247884.8629267939137
Winsorized Mean ( 10 / 20 )18605.1114754098214.54142574615686.720368389009
Winsorized Mean ( 11 / 20 )18599.9901639344204.74932420746890.8427426362954
Winsorized Mean ( 12 / 20 )18611.5573770492198.60215245256693.712767697693
Winsorized Mean ( 13 / 20 )18672.3803278689176.360484121785105.876213829027
Winsorized Mean ( 14 / 20 )18520.0557377049146.444530883941126.464645869106
Winsorized Mean ( 15 / 20 )18545.8508196721140.458714616078132.037736998835
Winsorized Mean ( 16 / 20 )18537.8770491803132.887524185369139.500507386391
Winsorized Mean ( 17 / 20 )18561.2868852459128.873330711665144.027369997708
Winsorized Mean ( 18 / 20 )18573.4442622951125.656894842447147.810784959974
Winsorized Mean ( 19 / 20 )18573.1016393443111.675139287703166.313664418141
Winsorized Mean ( 20 / 20 )18517.6262295082102.380813229312180.870083421124
Trimmed Mean ( 1 / 20 )18664.5576271186260.17170485925571.7393831785652
Trimmed Mean ( 2 / 20 )18651.1403508772250.82983387753274.3577431063628
Trimmed Mean ( 3 / 20 )18634.6909090909241.53726793150677.1503754624533
Trimmed Mean ( 4 / 20 )18615.1377358491234.62710033912279.339248147138
Trimmed Mean ( 5 / 20 )18593.9137254902226.71768311150382.0135133276986
Trimmed Mean ( 6 / 20 )18574.2217.80415959934285.2793630487493
Trimmed Mean ( 7 / 20 )18565.8723404255212.82754854142187.2343475629151
Trimmed Mean ( 8 / 20 )18555.2733333333207.00294716586489.637725391734
Trimmed Mean ( 9 / 20 )18541.1697674419200.08378628505392.667027707217
Trimmed Mean ( 10 / 20 )18529.9219512195192.45262532387396.283030278418
Trimmed Mean ( 11 / 20 )18518.1615384615183.551775345068100.887945668999
Trimmed Mean ( 12 / 20 )18505.8972972973174.324489013354106.157760174932
Trimmed Mean ( 13 / 20 )18490.5514285714163.358437488486113.190060537123
Trimmed Mean ( 14 / 20 )18464.6969696970154.678360227988119.374791292596
Trimmed Mean ( 15 / 20 )18456.9161290323151.863155228843121.536498443085
Trimmed Mean ( 16 / 20 )18444.4448275862149.000994193315123.787394355613
Trimmed Mean ( 17 / 20 )18431.2518518519146.5494363824125.768152418943
Trimmed Mean ( 18 / 20 )18412.588143.285689250532128.502630627724
Trimmed Mean ( 19 / 20 )18388.8869565217138.396113533865132.871411537304
Trimmed Mean ( 20 / 20 )18360.7238095238135.169835657425135.834476088713
Median18040.3
Midrange18882.9
Midmean - Weighted Average at Xnp18407.7433333333
Midmean - Weighted Average at X(n+1)p18456.9161290323
Midmean - Empirical Distribution Function18456.9161290323
Midmean - Empirical Distribution Function - Averaging18456.9161290323
Midmean - Empirical Distribution Function - Interpolation18456.9161290323
Midmean - Closest Observation18417.93125
Midmean - True Basic - Statistics Graphics Toolkit18456.9161290323
Midmean - MS Excel (old versions)18456.9161290323
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 18671.7163934426 & 277.60371859941 & 67.2603252133897 \tabularnewline
Geometric Mean & 18549.5284860081 &  &  \tabularnewline
Harmonic Mean & 18428.9071039383 &  &  \tabularnewline
Quadratic Mean & 18795.1276279776 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 18677.0950819672 & 267.767136430250 & 69.7512597362089 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 18680.8032786885 & 264.397090044245 & 70.6543452333852 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 18685.6573770492 & 254.849453304304 & 73.320374577133 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 18686.1163934426 & 252.797908759381 & 73.9172111238803 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 18673.0918032787 & 249.632357681476 & 74.802369279006 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 18612.6983606557 & 229.840717410420 & 80.9808573970797 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 18620.6049180328 & 227.429161894258 & 81.8743065442519 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 18634.8081967213 & 224.662652377286 & 82.945732187952 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 18609.2098360656 & 219.285505922478 & 84.8629267939137 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 18605.1114754098 & 214.541425746156 & 86.720368389009 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 18599.9901639344 & 204.749324207468 & 90.8427426362954 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 18611.5573770492 & 198.602152452566 & 93.712767697693 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 18672.3803278689 & 176.360484121785 & 105.876213829027 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 18520.0557377049 & 146.444530883941 & 126.464645869106 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 18545.8508196721 & 140.458714616078 & 132.037736998835 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 18537.8770491803 & 132.887524185369 & 139.500507386391 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 18561.2868852459 & 128.873330711665 & 144.027369997708 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 18573.4442622951 & 125.656894842447 & 147.810784959974 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 18573.1016393443 & 111.675139287703 & 166.313664418141 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 18517.6262295082 & 102.380813229312 & 180.870083421124 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 18664.5576271186 & 260.171704859255 & 71.7393831785652 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 18651.1403508772 & 250.829833877532 & 74.3577431063628 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 18634.6909090909 & 241.537267931506 & 77.1503754624533 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 18615.1377358491 & 234.627100339122 & 79.339248147138 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 18593.9137254902 & 226.717683111503 & 82.0135133276986 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 18574.2 & 217.804159599342 & 85.2793630487493 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 18565.8723404255 & 212.827548541421 & 87.2343475629151 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 18555.2733333333 & 207.002947165864 & 89.637725391734 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 18541.1697674419 & 200.083786285053 & 92.667027707217 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 18529.9219512195 & 192.452625323873 & 96.283030278418 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 18518.1615384615 & 183.551775345068 & 100.887945668999 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 18505.8972972973 & 174.324489013354 & 106.157760174932 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 18490.5514285714 & 163.358437488486 & 113.190060537123 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 18464.6969696970 & 154.678360227988 & 119.374791292596 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 18456.9161290323 & 151.863155228843 & 121.536498443085 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 18444.4448275862 & 149.000994193315 & 123.787394355613 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 18431.2518518519 & 146.5494363824 & 125.768152418943 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 18412.588 & 143.285689250532 & 128.502630627724 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 18388.8869565217 & 138.396113533865 & 132.871411537304 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 18360.7238095238 & 135.169835657425 & 135.834476088713 \tabularnewline
Median & 18040.3 &  &  \tabularnewline
Midrange & 18882.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 18407.7433333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 18456.9161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 18456.9161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 18456.9161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 18456.9161290323 &  &  \tabularnewline
Midmean - Closest Observation & 18417.93125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 18456.9161290323 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 18456.9161290323 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65886&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]18671.7163934426[/C][C]277.60371859941[/C][C]67.2603252133897[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]18549.5284860081[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]18428.9071039383[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]18795.1276279776[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]18677.0950819672[/C][C]267.767136430250[/C][C]69.7512597362089[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]18680.8032786885[/C][C]264.397090044245[/C][C]70.6543452333852[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]18685.6573770492[/C][C]254.849453304304[/C][C]73.320374577133[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]18686.1163934426[/C][C]252.797908759381[/C][C]73.9172111238803[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]18673.0918032787[/C][C]249.632357681476[/C][C]74.802369279006[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]18612.6983606557[/C][C]229.840717410420[/C][C]80.9808573970797[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]18620.6049180328[/C][C]227.429161894258[/C][C]81.8743065442519[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]18634.8081967213[/C][C]224.662652377286[/C][C]82.945732187952[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]18609.2098360656[/C][C]219.285505922478[/C][C]84.8629267939137[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]18605.1114754098[/C][C]214.541425746156[/C][C]86.720368389009[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]18599.9901639344[/C][C]204.749324207468[/C][C]90.8427426362954[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]18611.5573770492[/C][C]198.602152452566[/C][C]93.712767697693[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]18672.3803278689[/C][C]176.360484121785[/C][C]105.876213829027[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]18520.0557377049[/C][C]146.444530883941[/C][C]126.464645869106[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]18545.8508196721[/C][C]140.458714616078[/C][C]132.037736998835[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]18537.8770491803[/C][C]132.887524185369[/C][C]139.500507386391[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]18561.2868852459[/C][C]128.873330711665[/C][C]144.027369997708[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]18573.4442622951[/C][C]125.656894842447[/C][C]147.810784959974[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]18573.1016393443[/C][C]111.675139287703[/C][C]166.313664418141[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]18517.6262295082[/C][C]102.380813229312[/C][C]180.870083421124[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]18664.5576271186[/C][C]260.171704859255[/C][C]71.7393831785652[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]18651.1403508772[/C][C]250.829833877532[/C][C]74.3577431063628[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]18634.6909090909[/C][C]241.537267931506[/C][C]77.1503754624533[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]18615.1377358491[/C][C]234.627100339122[/C][C]79.339248147138[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]18593.9137254902[/C][C]226.717683111503[/C][C]82.0135133276986[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]18574.2[/C][C]217.804159599342[/C][C]85.2793630487493[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]18565.8723404255[/C][C]212.827548541421[/C][C]87.2343475629151[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]18555.2733333333[/C][C]207.002947165864[/C][C]89.637725391734[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]18541.1697674419[/C][C]200.083786285053[/C][C]92.667027707217[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]18529.9219512195[/C][C]192.452625323873[/C][C]96.283030278418[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]18518.1615384615[/C][C]183.551775345068[/C][C]100.887945668999[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]18505.8972972973[/C][C]174.324489013354[/C][C]106.157760174932[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]18490.5514285714[/C][C]163.358437488486[/C][C]113.190060537123[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]18464.6969696970[/C][C]154.678360227988[/C][C]119.374791292596[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]18456.9161290323[/C][C]151.863155228843[/C][C]121.536498443085[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]18444.4448275862[/C][C]149.000994193315[/C][C]123.787394355613[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]18431.2518518519[/C][C]146.5494363824[/C][C]125.768152418943[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]18412.588[/C][C]143.285689250532[/C][C]128.502630627724[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]18388.8869565217[/C][C]138.396113533865[/C][C]132.871411537304[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]18360.7238095238[/C][C]135.169835657425[/C][C]135.834476088713[/C][/ROW]
[ROW][C]Median[/C][C]18040.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]18882.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]18407.7433333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]18456.9161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]18456.9161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]18456.9161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]18456.9161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]18417.93125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]18456.9161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]18456.9161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65886&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65886&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean18671.7163934426277.6037185994167.2603252133897
Geometric Mean18549.5284860081
Harmonic Mean18428.9071039383
Quadratic Mean18795.1276279776
Winsorized Mean ( 1 / 20 )18677.0950819672267.76713643025069.7512597362089
Winsorized Mean ( 2 / 20 )18680.8032786885264.39709004424570.6543452333852
Winsorized Mean ( 3 / 20 )18685.6573770492254.84945330430473.320374577133
Winsorized Mean ( 4 / 20 )18686.1163934426252.79790875938173.9172111238803
Winsorized Mean ( 5 / 20 )18673.0918032787249.63235768147674.802369279006
Winsorized Mean ( 6 / 20 )18612.6983606557229.84071741042080.9808573970797
Winsorized Mean ( 7 / 20 )18620.6049180328227.42916189425881.8743065442519
Winsorized Mean ( 8 / 20 )18634.8081967213224.66265237728682.945732187952
Winsorized Mean ( 9 / 20 )18609.2098360656219.28550592247884.8629267939137
Winsorized Mean ( 10 / 20 )18605.1114754098214.54142574615686.720368389009
Winsorized Mean ( 11 / 20 )18599.9901639344204.74932420746890.8427426362954
Winsorized Mean ( 12 / 20 )18611.5573770492198.60215245256693.712767697693
Winsorized Mean ( 13 / 20 )18672.3803278689176.360484121785105.876213829027
Winsorized Mean ( 14 / 20 )18520.0557377049146.444530883941126.464645869106
Winsorized Mean ( 15 / 20 )18545.8508196721140.458714616078132.037736998835
Winsorized Mean ( 16 / 20 )18537.8770491803132.887524185369139.500507386391
Winsorized Mean ( 17 / 20 )18561.2868852459128.873330711665144.027369997708
Winsorized Mean ( 18 / 20 )18573.4442622951125.656894842447147.810784959974
Winsorized Mean ( 19 / 20 )18573.1016393443111.675139287703166.313664418141
Winsorized Mean ( 20 / 20 )18517.6262295082102.380813229312180.870083421124
Trimmed Mean ( 1 / 20 )18664.5576271186260.17170485925571.7393831785652
Trimmed Mean ( 2 / 20 )18651.1403508772250.82983387753274.3577431063628
Trimmed Mean ( 3 / 20 )18634.6909090909241.53726793150677.1503754624533
Trimmed Mean ( 4 / 20 )18615.1377358491234.62710033912279.339248147138
Trimmed Mean ( 5 / 20 )18593.9137254902226.71768311150382.0135133276986
Trimmed Mean ( 6 / 20 )18574.2217.80415959934285.2793630487493
Trimmed Mean ( 7 / 20 )18565.8723404255212.82754854142187.2343475629151
Trimmed Mean ( 8 / 20 )18555.2733333333207.00294716586489.637725391734
Trimmed Mean ( 9 / 20 )18541.1697674419200.08378628505392.667027707217
Trimmed Mean ( 10 / 20 )18529.9219512195192.45262532387396.283030278418
Trimmed Mean ( 11 / 20 )18518.1615384615183.551775345068100.887945668999
Trimmed Mean ( 12 / 20 )18505.8972972973174.324489013354106.157760174932
Trimmed Mean ( 13 / 20 )18490.5514285714163.358437488486113.190060537123
Trimmed Mean ( 14 / 20 )18464.6969696970154.678360227988119.374791292596
Trimmed Mean ( 15 / 20 )18456.9161290323151.863155228843121.536498443085
Trimmed Mean ( 16 / 20 )18444.4448275862149.000994193315123.787394355613
Trimmed Mean ( 17 / 20 )18431.2518518519146.5494363824125.768152418943
Trimmed Mean ( 18 / 20 )18412.588143.285689250532128.502630627724
Trimmed Mean ( 19 / 20 )18388.8869565217138.396113533865132.871411537304
Trimmed Mean ( 20 / 20 )18360.7238095238135.169835657425135.834476088713
Median18040.3
Midrange18882.9
Midmean - Weighted Average at Xnp18407.7433333333
Midmean - Weighted Average at X(n+1)p18456.9161290323
Midmean - Empirical Distribution Function18456.9161290323
Midmean - Empirical Distribution Function - Averaging18456.9161290323
Midmean - Empirical Distribution Function - Interpolation18456.9161290323
Midmean - Closest Observation18417.93125
Midmean - True Basic - Statistics Graphics Toolkit18456.9161290323
Midmean - MS Excel (old versions)18456.9161290323
Number of observations61



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')